Aim. Improvements of the methods of approximation of settling by exponential, finely-rational, polynomial, and sinusoidal functions with the definition of intervals between observation cycles. Methods and results of the work. The methods of approximation and prognostication of settling of control benchmarks of building are examined. Special attention is given to the exponential function with the use of simple and exact method of determination of coefficient of intensity of settling using the mean values of the settling and time intervals, which allows substantially a decrease in the volume of iteration calculations. The exact (integral) method of determination coefficient of intensity of settling offered in the article allows to practically withdraw the iteration process of calculation and to specify aspect or soil porosity ratios, which are determined from laboratory soil researches using data of approximation of settling. For replacement of methods of polynomial and sinusoid the algorithm of approximation of settling is worked out by the method of finely-rational function, proposed by Ziborov [Ziborov, 1972], and methods of determination of inter cyclical intervals for the execution of rational monitoring observations on vertical displacements of buildings. Efficiency of application of method of finely-rational function and practical pointlessness of the use of the polynomial and sinusoid for approximation of settling function is shown. Scientific novelty. The executed improvements promote efficiency and repressiveness of the approximation data, and assist diminishing calculations volume. Practical value. Consists in development of the method for calculation of time intervals between observation cycles for the different functions of approximation, which practically allows excluding the iteration process of determination of the coefficient of intensity of settling for exponent and using of this coefficient for clarification of coefficients of compressibility or soil porosity, which are determined using its laboratory researches. It is proven, that the method of finely-rational function (FRF) proposed in [Ziborov, 2004], is simplest in the organization of calculations.
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